Integrating the Structural Auction Approach and Traditional Measures of Market Power

(2.16) reduces to C(y_i^r) = α_km y_i^r + λ_ky_i^rt + β_k(y_i^r)²,which is simply a quadratic cost
function.

The industry marginal costc(Y^r), required to estimate industry-level markups
represented by equation (2.13), is obtained in the following way. First, we differentiate
packer’s processing cost equation (2.16) with respect to output to get a firm-level
marginal cost, as c(y^r_i ) = ∂C(y^r_i )/∂y_i^r = β₀ + 2β_λky^r_i . For convenience, industry
marginal cost can simply be represented as:
(2.19)                                  c( yr ) = 2 yr.

Next, we obtain the industry marginal cost equation by multiplying every term of (2.19)
by each firm’s market share s_i , and summing across all processors in the industry, as:

∑_isic(yi^r)=2∑_isiyi^r,

which can be re-arranged to yield the industry marginal cost function, c(Y^r), as:

(2.20)                            c(Y^r ) = 2Y^rHHI.

Lastly, the industry pricing equation used to estimate oligopsony power is
obtained by re-arranging equation (2.9a), after replacing c(Y ^r) with equation (2.20), as:
(2.9b)                 p^r = p^f [1 + ^{(1 + &)HHI} ] + 2γ^fHHi,

^εs

where δ is a transaction level average bid shading estimated with the structural auction
approach described previously.

Empirical estimation of equation (2.9b) also requires knowing the elasticity of
cattle supply. The elasticity of cattle supply could be obtained from a cattle supply
equation, which is estimated jointly with equation (2.9b). However, a system of

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